Back in December, I posted about an original argument against the legitimacy of the state, which I called The Self-Confidence Argument for Philosophical Anarchism. Here’s the argument, again:

1. This argument is a valid deductive argument. (Premise.)
2. If this argument is a valid deductive argument and all of its premises are true, then its conclusion is true. (Premise.)
3. Its conclusion is No state could possibly have legitimate political authority. (Premise.)
4. If No state could possibly have legitimate political authority is true, then no state could possibly have legitimate political authority. (Premise.)
5. All of this argument’s premises are true. (Premise.)
6. This is a valid deductive argument and all of its premises are true. (Conj. 1, 5)
7. Its conclusion is true. (MP 2, 6)
8. No state could possibly have legitimate political authority is true. (Subst. 3, 7)
9. ∴ No state could possibly have legitimate political authority. (MP 4, 8)

Q.E.D., and smash the state.

The problem, of course, is that if this argument is sound, then it seems like you could construct another argument that must also sound, simply by substituting Some states have legitimate political authority everywhere in lines 3, 4, 8 and 9 that No state could possibly have legitimate political authority. And then you’d get an apparently perfectly sound Self-Confidence Argument for the State. It’s easy enough to figure out that there has to be something wrong with at least one of those arguments. Their conclusions directly contradict each other, and so couldn’t both be true. But they are formally completely identical; so presumably whatever is wrong with one argument would also be wrong with the other one. But if so, what’s wrong with them? Are they invalid? If so, how? Whichever argument you choose to look at, the argument has only four inferential steps, and all of them use elementary valid rules of inference or rules of replacement. Since each inferential step in the argument is valid, the argument as a whole must be valid. This also, incidentally, provides us with a reason to conclude that premise 1 is true in both. Premise 2 seems true by definition, under any standard definition of deductive validity. Premise 3 is a simple empirical observation. If you’re not sure it’s true, you can just look down the page to line 9 and find out. Premise 4 is a completely uncontroversial application of standard disquotation rules for true sentences. That seems to leave Premise (5). And premise (5) may seem over-confident, perhaps even boastful. But what it says is that just all the premises of the argument are true; so if it’s false, then which premise of the argument are you willing to deny? Whichever one you pick, what is it that makes that premise false? On what (non-question-begging) grounds would you say that it is false?

On my first post, a commenter named Lexi made the following observation, in order to suggest that you might nevertheless be able to reject Premise 5 — they noted that Premise 5 makes a statement about the truth of all the premises in the argument. But one of the premises it makes the claim about is Premise 5 itself. And perhaps that allows you to cut the knot:

Premise 5 is, at least, unsupportable. In order for all the premises to be true, premise 5 must also be true. The only way to justify premise 5 is by circular reasoning. Given that, maybe it's not so surprising that you can support any conclusion X with the argument, since circular reasoning can establish any proposition as true.

–Lexi, comment (23 December 2015)

They’re certainly right to observe since premise 5 itself is among the statements premise 5 is quantifying over, its truth conditions would have to be something like:

(T₅) Premise 5 is true ≡ Premise 1 is true & Premise 2 is true & Premise 3 is true & Premise 4 is true & Premise 5 is true

That might seem curious, and it involves a certain sort of circularity, but I can’t say I see how it makes the premise insupportable, if that is supposed to mean that you couldn’t give non-circular reasons to believe that Premise 5 is true.

After all, statements like this really are a part of ordinary language in non-philosophical cases. For example, Marco Polo begins his Description of the World by making the following statement in the Prologue:

. . . We will set down things seen as seen, things heard as heard, so that our book may be an accurate record, free from any sort of fabrication. And all who read this book or hear it may do so with full confidence, because it contains nothing but the truth.

This is a pretty common conceit in traveler’s tales: the author frequently assures the reader that everything they say — incredible as it might seem — is true.

But that statement is among the statements in Polo’s book; if he asserts that it contains nothing but the truth, then that sentence, inter alia, asserts that it is itself true:

(M) Marco Polo and his brothers traveled the Silk Road to China, and there he befriended the Emperor Kublai Khan, and along the way they observed the decadent customs of Lesser Armenia, and along the way they traveled among the Turkomans, and . . ., and (M) is true.

Which makes its truth-conditions something like:

(T_M) (M) is true ≡ Marco Polo and his brothers did travel the Silk Road to China, and there he did befriend the Emperor Kublai Khan, and along the way they did observe the decadent customs of Lesser Armenia, and along the way they did travel among the Turkomans, and . . ., and (M) is true.

But here’s the thing. It doesn’t seem to me like (M) is insupportable or viciously circular. In ordinary cases, wouldn’t we determine whether it’s true or not by going through the book and checking out the other statements? I.e., some people reading the book might take everything else Marco Polo says there as true; and if so, then they’d take (M) as true as well. Call someone with this attitude towards (M) and its truth-conditions the True Believer. On the other hand, some people doubt parts of his tale — some people for example doubt that he even went to China at all. If so, they typically think not only that the first conjunct is false, but also the last one — if one of his statements is an assurance that all the statements are true, and any of the other statements are false, then that makes at least two falsehoods in total. Call someone with this attitude towards (M) and its truth-conditions the Normal Skeptic.

But now imagine a reader who insisted that they were a skeptic about Polo’s claims — but then, when asked one-by-one, signed off on every one of his other statements, except that they denied the statement that the book contains nothing but the truth. Call someone who takes this attitude towards (M) and its truth-conditions the Degenerate-Case Skeptic. Would Degenerate-Case Skepticism even make sense, as a position you might take with respect to the truth value of the claims in the book? Would it be a supportable claim? If so, how? If anything, it seems like the fault of circular here is most easily attributed to someone who denies (M), or who mutatis mutandis denies Premise (5), based solely on Degenerate-Case skepticism. If (M) or (5) is false for no other reason that you even in principle could give other than its sui generis falsity, then that seems like a particularly radical form of question-begging.

Of course, you might say that it is insupportable, but so is the alternative, the True Believer’s claim that all the statements are true. So there’s no non-question-begging reason you could give to say that (M) or (5) is true, and there’s no non-question-begging reason you could give to say that (M) or (5) is false. Since the function of an argument is to give reasons to believe that its conclusion is true, if one of the premises cannot have any non-question-begging reason given either for its truth or falsity, then it seems like the argument can’t provide reasons for any conclusions that depend logically on that premise. (As the conclusion of any Self-Confidence Argument does; the Conj. in the first inferential step cites Premise 5, and everything else follows from that.) So you could say that. But now the question is, why say that? Isn’t it normally possible to give reasons for being a True Believer, and reasons for being a Normal Skeptic, even if there are no reasons you can give for being a Degenerate-Case skeptic? Is this kind of claim of radical insupportability the way we normally read texts that make assurances about themselves, like Marco Polo? Should it be?

If it’s not, and it shouldn’t, then should it be the way that we read Premise 5 here, even though it’s not the way we read Marco Polo? If there’s some difference between the two, that suggests reading Marco Polo in this way but not reading Premise 5 in this way, then what if any reason (preferably a principled reason that’s not question begging, and not simply ad hoc) could we give for the difference in semantic treatment?^[1]

1. ^[1]Or is it a difference in their semantics? Or a difference in something else, e.g. the pragmatics of their use?↩

[This originally appeared as a guest post that I wrote for Richard Chappell’s blog Philosophy, et cetera]

Here’s one of the few canonical philosophical puzzles that I had learned about by the age of five. What’s the truth-value of the following statement?

(L) This statement (L) is false.

The problem, of course, is that if (L) is true then it’s false, and if (L) is false then it’s true. Thus, any theory of truth that assigns a truth-value to (L) is internally contradictory, since the theory will (inter alia) include the contradictory truth-ascription:

(TL) L is true if and only if L is false.

Since there are no true contradictions, a theory of truth must not assign any truth-value to (L) at all. But how do you doing it? If a statement hasn’t got a truth-value, then the usual take is that they are, in some respect, nonsense; that is, they fail to make an assertion — just as “Cat mat on the sat the” fails to make an assertion. The canonical approach to (L) in the 20th century has been to try to come up with some principled means of ruling (L) out of the language by means of setting up the right structure of rules beforehand (just as you can point to the preexisting rules of syntax to show that “Cat mat on the sat the” doesn’t amount to a complete sentence). The most famous attempt, and the inspiration of many of the subsequent attempts, has been Tarski’s attempt to sidestep the Liar Paradox by means of segmenting language into object-language and meta-language layers. The idea being that, if you do this assiduously, you can avoid self-referential paradoxes because self-reference won’t be possible in languages whose sentences can be ascribed truth-values; because they can only be ascribed truth-values within a meta-language that contains the names of the object language’s sentences and truth-predicates for those sentences. I have a lot of problems with this approach; a full explanation of them is something that I ought to spell out (indeed, have spelled out) elsewhere. But here’s a quick gloss of one of the reasons: Tarski and the people inspired by him started setting up ex ante rules to try to rule out self-referential sentences because it’s self-reference that makes the Liar Paradox paradoxical (and that makes for similar paradoxes in similar sentences; exercise for the reader: show how “If this sentence is true, then God exists” is both necessarily true and strictly entails the existence of God). But there’s an obvious and general problem for the method: there are self-referential sentences which are unparadoxical, and indeed self-referential sentences which are true. Here’s an example which may or may not cause trouble for Tarskian theories, depending on the details:

(E) This sentence (E) is in English.

(E) is truth-valuable; and in fact it is true. (If, on the other hand, it had said “This sentence is in French,” it would have been false.) Now, this may cause trouble for the Tarskian method and it may not, depending on the details of a particular account. (Sometimes people want to ban all self-referential sentences; sometimes they are more careful and claim that object languages might be able to name their own sentences but only so long as they don’t contain the truth-predicates for their own language.) But even if (E) is allowed, you haven’t solved the problem. There are plenty of self-referential truth-ascribing sentences that aren’t paradoxical, too. Here’s one:

(EM) Either this sentence (EM) is true, or this sentence (EM) is false.

Unlike (L), this causes no logical paradoxes. If you suppose that it’s false, that means that it turns out to be true — since the second disjunct, “this sentence (EM) is false” turns out to be true; meaning that it cannot be false. But it can be true, without contradiction. So it has to be true, if it has any truth-value at all. That shouldn’t be surprising; it’s an instance of the law of the excluded middle, and all instances of the law of the excluded middle are true.

Now, you might think that (EM)’s relationship to ordinary talk is attenuated enough, and the reasons for thinking it unparadoxical are technical enough, that it might be an acceptable loss if some other technical stuff that saves us from (L) happens to rule out (EM) too. I’d be inclined to agree, except that (EM) isn’t the only example I had up my sleeve, either. Here’s another. In the Prologue to the Travels, Marco Polo wrote,

We will set down things seen as seen, things heard as heard, so that our book may be an accurate record, free from any sort of fabrication. And all who read this book or hear it may do so with full confidence, because it contains nothing but the truth.

Let M be the conjunction of all the assertions that Marco Polo makes in his book. The book contains nothing but the truth if and only if M is true, but that the book contains nothing but the truth is one of the many assertions in the book, so “M is true” is one of the conjuncts of M. Thus:

(M) This conjunction (M) is true, and Marco Polo traveled the Silk Road to Cathay, and served in the court of the Great Khan, and observed the barbarous customs of lesser Armenia, and … and … and ….

But it’s either true or false that Marco Polo’s book contains nothing but the truth; that assertion is a standard bit of understood language (passages just like it are a near-universal feature of traveler’s tales, or other extraordinary stories where the author feels the need to reassure you that she’s not making things up). If your theory of language throws it out as nonsense, then your “theory of language” needs to be thrown out, on the grounds that it’s not semantically serious. (Whatever it’s a theory of may be interesting, but it’s something other than language as it actually exists.)

Now, like Polo, I may have been fudging just a bit in what I said. I suggested that M isn’t paradoxical; I don’t think it is, but there is a way to make it seem paradoxical. Lots of readers have doubted that Polo was telling the truth; some of them, for example, were unimpressed by the evidence that he had ever served in the court of the Great Khan; others weren’t so sure about the tales of dog-headed men or giant birds that consumed elephants. Whatever the case, they believed that Marco Polo made at least two false assertions in his book: (1) the claim about his journeys that they doubted, and (2) the claim that his book contained nothing but the truth. Call these the normal skeptics. I’m sure there were also a few readers (however credulous they would have to have been), who believed that the Travels really did contain nothing but the truth; that is, that there were no false assertions in the book, including the assertion that the book contained no false assertions. Call these the normal believers. But now imagine a third kind of reader, a perverse skeptic — a philosopher, of course — who noticed that you could gloss the contents of the book as M, and who decided that she believed everything that Polo said in the book about his journeys, from the customs of lesser Armenia to the domains of the Great Khan to the giant birds. She believes everything in the book, except … there is one assertion that she thinks is false — that is, (1) the assertion that everything in the book is true, and nothing else.

There are a couple of different ways that you could approach the difficulty. One way is to point out that the perverse skeptic really is being perverse. That’s just not how you can sensibly read the book. Either you think that nothing in the book is false, or you think that at least two things are; the assurance of truthfulness just can’t be a candidate for falseness until something else has been shown false. But if you list the truth-conditions of M, then “M is true” is one among them, and it’s hard to see how you could stop the perverse skeptic from going down the list and picking that one as the only one to be false. Certainly Polo doesn’t say “The rest of the book besides this sentence contains nothing but the truth.” And given that he did say what he did, I’d be hard put to say that “this book contains nothing but the truth” isn’t one of the untruths denied by the sentence, if something else in the book is false.

Another way to approach it is this: you can imagine an argument between the normal skeptic and the normal believer; whether or not one ever managed to convince the other in the end, you can in principle identify the sorts of reasons that they might offer to try to determine whether Polo really did tell the truth about the birds, or about the Khan, or…, and you can say what things would be like if one or the other is true. But what kind of argument could the normal believer and the perverse skeptic have? How would one convince the other? Or, to take it beyond the merely psychological point to the epistemological point, what kind of reasons could the normal believer possibly give to the perverse skeptic to give up the belief that “this book contains nothing but the truth” is false? (She can’t point to all the true statements about his journey; the perverse skeptic already believes in those.) Or, to take it beyond the epistemological point to the ontological point: what sort of truth-makers could even in principle determine whether the normal believer or the perverse skeptic is in the right?

So there is a problem with M, to be sure. But the problem is not the same as the problem posed by L: there’s no logical contradiction involved, so its self-referentiality sets off no logical explosions. And the solution can’t be the same either: the radical move of abandoning the sentence as meaningless works with (L), where there’s just no right way to take it, but it doesn’t help us out with (M), where there obviously is a right way to take it (i.e., as the normal readers take it, and not as the perverse reader takes it).

So there has to be some right way to go about ascribing a truth-value to (M) (and also (E)). Whatever it is, it may very well also explain how we can ascribe a truth-value to (EM). But it certainly cannot also mean that we try to ascribe a truth-value to (L). What is it? Is there some kind of principled and motivated general rule that we can add to our logical grammar, so as to get M and E and maybe EM but no L? If so, what in the world would it be? If not, then what do we do?

(I have my own answers; for the details, you can look up Sentences That Can’t Be Said in the upcoming issue of Southwest Philosophy Review. Or contact me if you’re interested enough to want a copy of the essay. But I want to pose the puzzle and see what y’all think about it as it stands.)

Update 2005-12-08: I fixed a minor error in phrasing. Thanks to Blar for pointing it out in comments.